Compound Interest When we save with a bank the bank pays us interest at the end of each year. If we leave the money alone then the interest gets added to our balance giving us a bigger balance. The next time we calculate the interest it is a % of a larger sum than before. Example Suppose we put £500 into an account which pays a rate of 4% per annum. How much is this worth after 3 years? How much interest do we get for the 3 years?

Long Method 4% = 0.04 Int in year 1 = 0.04 X £500 = £20 Balance after 1st year = £520 Int in year 2 = 0.04 X £520 = £20.80 Balance after 2nd year = £540.80 Int in year 3 = 0.04 X £540.80 = £21.632 = £21.63 Balance after 3rd year = £562.43 Interest gained in 3 years = £562.43 - £500 = £62.43

Quick Method Adding 4% gives us 104% or 1.04 so Balance after year 1 = 1.04 X £500 = £520 Balance after year 2 = 1.04 X £520 = £540.80 Balance after year 3 = 1.04 X £540.80 = £562.432 = £ 562.43 Again total interest = £62.43

Really Quick Method Adding 4% gives us 104% or 1.04 We multiply by 1.04 on three occasions so Balance after year 3 = 1.04 X 1.04 X 1.04 X £500 = (1.04)3 X £500 = £562.432 = £ 562.43 Use the xy button Again total interest = £62.43

APPRECIATION - Growing in value. Example When it is growing a baby shark’s weight increases by 18% per week. If a baby shark is currently 40kg then how heavy will it be in 5 weeks time ? (to the nearest kg) ****************** 18% more gives us 118% or 1.18 Weight in 5 weeks = 1.18 X 1.18 X 1.18 X 1.18 X 1.18 X 40kg = 91.51…kg = 92kg

DEPRECIATION - Loss of value. Example For each km you climb a mountain the amount of oxygen in the air becomes 13% less. The air at ground level contains 20 units of oxygen. How many units will there be at the top of Mount Everest which is 8km high? ****************** 13% less gives us 87% or 0.87 . Oxygen level = 0.87 X 0.87 X 0.87 X 0.87 X 0.87 X 0.87 X 0.87 X 0.87 X 20 units = 6.56 units Hence need for masks!!

Example The Simpsons buy a house for £80000. The following year it is worth £84000. What is the rate of appreciation? ************ Actual increase = £84000 - £80000 = £4000 % increase = 400080000 = 0.05 or 5%

Example On its first bounce a pogo stick reaches a height of 48cm. On its second bounce it only reaches a height of 42cm. What is the % depreciation in height? ************* Actual change = 48 – 42 = 6 % change = 6  48 = 0.125 or 12.5%

Example A car completes one lap of a track at 87mph. It then completes a second lap at 78mph. Find the % drop in speed! ************* Actual drop = 87 - 78 = 9 mph % drop = 9  87 = 0.1034….. = 0.103 = 10.3%

Example The population of town is 36000. This is expected to rise by 8% per annum over the next five years. *********** 8% more = 108% or 1.08 Pop in 5 years = 36000 X 1.08 X 1.08 X 1.08 X 1.08 X 1.08 OR = 36000 X (1.08)5 = 52895.8... = 52900 To nearest 100.